//Given a sorted integer array nums and an integer n, add/patch elements to the 
//array such that any number in the range [1, n] inclusive can be formed by the su
//m of some elements in the array. 
//
// Return the minimum number of patches required. 
//
// 
// Example 1: 
//
// 
//Input: nums = [1,3], n = 6
//Output: 1
//Explanation:
//Combinations of nums are [1], [3], [1,3], which form possible sums of: 1, 3, 4
//.
//Now if we add/patch 2 to nums, the combinations are: [1], [2], [3], [1,3], [2,
//3], [1,2,3].
//Possible sums are 1, 2, 3, 4, 5, 6, which now covers the range [1, 6].
//So we only need 1 patch.
// 
//
// Example 2: 
//
// 
//Input: nums = [1,5,10], n = 20
//Output: 2
//Explanation: The two patches can be [2, 4].
// 
//
// Example 3: 
//
// 
//Input: nums = [1,2,2], n = 5
//Output: 0
// 
//
// 
// Constraints: 
//
// 
// 1 <= nums.length <= 1000 
// 1 <= nums[i] <= 104 
// nums is sorted in ascending order. 
// 1 <= n <= 231 - 1 
// 
// Related Topics 贪心 数组 
// 👍 302 👎 0


package leetcode.editor.cn;

//Java：Patching Array
public class P330PatchingArray {
    public static void main(String[] args) {
        Solution solution = new P330PatchingArray().new Solution();
        solution.minPatches(new int[]{1, 5, 10}, 20);

        // TO TEST
    }

    //leetcode submit region begin(Prohibit modification and deletion)
    class Solution {
        public int minPatches(int[] nums, int n) {
            int patches = 0;
            long x = 1;
            int length = nums.length, index = 0;
            while (x <= n) {
                if (index < length && nums[index] <= x) {
                    x += nums[index];
                    index++;
                } else {
                    x *= 2;
                    patches++;
                }
            }
            return patches;
        }
    }
//leetcode submit region end(Prohibit modification and deletion)

}